Bitwise operators - The Journey

If you are trying to search for bitwise operators on the web, you will find loads of information. However, when I was learning about bitwise operations, none of those resources could clarify my understanding. Finally, I have found a way that is easier and faster to understand bitwise operations. I hope it will help you as well.

The bitwise table

The table above represents the chain of bits that we have. This table will be our guide through the bitwise world. Before we continue, just have a look at the table and see that if we sum up all the values, we will have 255, which means it is the highest value of a bit.

Nevertheless, to achieve 255, all the bits in the table must be true (1).

A few more examples:

Is it easier with the table? What we did is really simple: we took a random number between 0 and 255 and applied it to the table to see its representation in binary. Now we know that 5 in binary is 101 and 10 is 1010.

The & (AND) operator

Here our table become a amazing tool to use. The operator & by definition says: “Bits that are set in both $a and $b are set.” (source). With that definition what will be the result of  the following expression:

<?php
echo (5 & 3);

Let’s start with the table where we now have the bitwise operator on the leftmost and the result on the rightmost.

Using the operator AND, the result of our operation (5 & 3) is 1.

The | (OR) operator

To use the OR operator we will take the same example we used in the AND operator to understand the difference. By definition we have: “Bits that are set in either $a or $b are set.”

<?php
echo (5 | 3);

Applying the documentation definition to the bitwise table should look something like this:

This time, the result is 7.

The ^ (XOR) operator

Finally, we are at the XOR operator. It is close to the OR operator but with a big difference. Let’s see what the definition says: “Bits that are set in $a or $b but not both are set.”

<?php
echo (5 ^ 3);

Can you guess what is the output of the operation (5 ^ 3)?

Yes, that is right! It is 6.